1. Field of the Invention
This invention relates generally to a packing arrangement for bodies having circular cross-sections, and more particularly to a close packing arrangement for bodies having circular cross-sections of three different radii.
2. Description of Related Art
Packing of bodies having equal circular cross-sections, such as cans of food, is normally performed in an egg crate type manner so that the centers of four adjacent circles are located at the vertices of a square to give an overall rectangular configuration. It is also well known to offset one tier or row of these circular cross-sectioned bodies from the next so that the centers of four adjacent circles are located at the vertices of a parallelepiped to give a more dense or close packing.
Close packing of spheres of equal size is performed one way in a cubic close packing where twelve spheres are arranged to form a cube having three tiers of four spheres, with the center tier offset from the top and bottom tiers. In infinite aggregations of a cubic close packing arrangement each sphere contacts twelve other spheres. In addition to the cubic close packing, a hexagonal close packing arrangement of equal sized spheres is known. Robert Williams in a book entitled "The Geometrical Foundation of Natural Structure, A Source Book of Design", Dover Publications, Inc., 1979, provides descriptions of these arrangements.
In "Solid Geometry", L. Lines, Dover Books, 1965, in Chapter 14--Sphere Packs, the definition is given: "If an infinite number of equal spheres are arranged so that every sphere is similarly related to the rest and in contact with at least four of them, they are said to form a sphere pack."
All of the foregoing arrangements relate to bodies having equal circular cross-sections. No similar descriptions relating to packing arrangements of bodies having unequal circular cross-sections have been located.
The present invention involves packing arrangements for bodies having three different circular cross-sections, which provide a close packing.
It is therefore an object of this invention to provide a packing arrangement for bodies having circular cross-sections, and radii in the ratio of one, two and three.
It is a further object of this invention to provide a packing arrangement for bodies which, while not having circular cross-sections precisely, approximate circular cross-sections, and have radii for such approximate cross-sections in the ratio of one, two and three.
It is also an object of this invention to define certain particularly useful packing arrangements of bodies having circular cross-sections or approximations thereof and radii in the ratio of one, two and three.
It is a further object of this invention to provide a basic sphere packing arrangement using spheres having radii in the ratio of one, two and three.
It is a still further object to provide such a sphere packing arrangement which can be expanded with successive layers to form a sphere pack.
In accordance with these and other objects, which will become apparent hereafter, the instant invention will now be described with reference to the accompanying drawings.